Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No: 301.05123
Autor: Erdös, Paul
Title: Extremal problems on graphs and hypergraphs. (In English)
Source: Proc. 1rst Working Sem. Hypergraphs, Columbus 1972, Lecture Notes Math. 411, 75-84 (1974).
Review: [For the entire collection see Zbl 282.00007.]
This survey paper continues the line of questioning of the author's earlier papers, for example in Theory Graphs Appl., Proc. Sympos. Smolenice 1963, 29-36 (1964; Zbl 161.20501), and, in Chapter II, generalizes some of the questions from graphs to hypergraphs. If \underline{G} is a finite family of r-graphs (i.e. r-uniform hypergraphs), then f(n; \underline{G}) is defined to be the smallest integer m such that every r-graph with n vertices and at least mr-edges contains a sub-r-graph isomorphic to a member of \underline{G}. When \underline{G} is a family of ordinary graphs, it is known from the theorems of P. Erdös and A. H. Stone [Bull. Amer. math. Soc. 52, 1087-1091 (1946; Zbl 063.01277)] und P. Erdös and M. Simonovits [Stud. Sci. Math. Hung. 1, 51-57 (1966; Zbl 178.27301)] that